PhaseAdjuster.java

package org.drip.numerical.fourier;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * Copyright (C) 2015 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
 *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
 *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
 *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
 *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
 *      and computational support.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
 * 
 *  DROP Product Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Loan Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Asset Liability Management Analytics
 *  - Capital Estimation Analytics
 *  - Exposure Analytics
 *  - Margin Analytics
 *  - XVA Analytics
 * 
 *  DROP Computational Core implements libraries for the following:
 *  - Algorithm Support
 *  - Computation Support
 *  - Function Analysis
 *  - Model Validation
 *  - Numerical Analysis
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Statistical Learning
 * 
 *  Documentation for DROP is Spread Over:
 * 
 *  - Main                     => https://lakshmidrip.github.io/DROP/
 *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
 *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
 *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
 *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
 *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
 *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
 *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
 *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
 *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *      you may not use this file except in compliance with the License.
 *   
 *  You may obtain a copy of the License at
 *      http://www.apache.org/licenses/LICENSE-2.0
 *  
 *  Unless required by applicable law or agreed to in writing, software
 *      distributed under the License is distributed on an "AS IS" BASIS,
 *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  
 *  See the License for the specific language governing permissions and
 *      limitations under the License.
 */

/**
 * <i>PhaseAdjuster</i> implements the functionality specifically meant for enhancing stability of the
 * Fourier numerical Routines.
 * 
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/README.md">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/fourier/README.md">Specific Fourier Transform Functionality - Rotation Counter, Phase Adjuster</a></li>
 *  </ul>
 * <br><br>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class PhaseAdjuster {

    /**
     * No Multi-Valued Principal Branch Tracking
     */

    public static final int MULTI_VALUE_BRANCH_PHASE_TRACKER_NONE = 0;

    /**
     * Multi-Valued Logarithm Principal Branch Tracking Using Rotating Counting
     */

    public static final int MULTI_VALUE_BRANCH_PHASE_TRACKER_ROTATION_COUNT = 1;

    /**
     * Multi-Valued Logarithm PLUS Power Principal Branch Tracking Using the Kahl-Jackel Algorithm
     */

    public static final int MULTI_VALUE_BRANCH_POWER_PHASE_TRACKER_KAHL_JACKEL = 2;

    /**
     * Handling the Branch Switching of the Complex Power Function according Kahl-Jackel algorithm:
     *  - http://www.pjaeckel.webspace.virginmedia.com/NotSoComplexLogarithmsInTheHestonModel.pdf
     * 
     * @param cnGNumerator The Log G Numerator
     * @param cnGDenominator The Log G Denominator
     * @param iN Number of Numerator Counted rotations
     * @param iM Number of Numerator Counted rotations
     * 
     * @return The Branch Switching Log Adjustment
     */

    public static final org.drip.function.definition.CartesianComplexNumber PowerLogPhaseTracker (
        final org.drip.function.definition.CartesianComplexNumber cnGNumerator,
        final org.drip.function.definition.CartesianComplexNumber cnGDenominator,
        final int iN,
        final int iM)
    {
        if (null == cnGNumerator || null == cnGNumerator || iN < 0 || iM < 0) return null;

        double dblAbsDenominator = cnGDenominator.abs();

        if (0. == dblAbsDenominator) return null;

        try {
            return new org.drip.function.definition.CartesianComplexNumber (java.lang.Math.log (cnGNumerator.abs() /
                dblAbsDenominator), cnGNumerator.argument() - cnGDenominator.argument() + 2. *
                    java.lang.Math.PI * (iN - iM));
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }
}